# std::logb, std::logbf, std::logbl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float logb ( float num ); double logb ( double num ); long double logb ( long double num ); |  | (until C++23)
constexpr /*floating-point-type*/ logb ( /*floating-point-type*/ num ); |  | (since C++23)
float logbf( float num ); | (2) | (since C++11) (constexpr since C++23)
long double logbl( long double num ); | (3) | (since C++11) (constexpr since C++23)
SIMD overload (since C++26) |  |
Defined in header `<simd>` |  |
template< /*math-floating-point*/ V > constexpr /*deduced-simd-t*/<V> logb ( const V& v_num ); | (S) | (since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double logb ( Integer num ); | (A) | (constexpr since C++23)

1-3) Extracts the value of the unbiased radix-independent exponent from the floating-point argument num, and returns it as a floating-point value. The library provides overloads of `std::logb` for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise `std::logb` on v_num. (See `math-floating-point` and `deduced-simd-t` for their definitions.) | (since C++26)

A) Additional overloads are provided for all integer types, which are treated as double. | (since C++11)

Formally, the unbiased exponent is the signed integral part of logr|num| (returned by this function as a floating-point value), for non-zero num, where r is std::numeric_limits<T>::radix and `T` is the floating-point type of num. If num is subnormal, it is treated as though it was normalized.

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, the unbiased exponent of num is returned as a signed floating-point value.

If a domain error occurs, an implementation-defined value is returned.

If a pole error occurs, -HUGE_VAL, `-HUGE_VALF`, or `-HUGE_VALL` is returned.

### Error handling

Errors are reported as specified in math_errhandling.

Domain or range error may occur if num is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- If num is ±0, -∞ is returned and FE_DIVBYZERO is raised.
- If num is ±∞, +∞ is returned.
- If num is NaN, NaN is returned.
- In all other cases, the result is exact (FE_INEXACT is never raised) and the current rounding mode is ignored.

### Notes

POSIX requires that a pole error occurs if num is ±0.

The value of the exponent returned by `std::logb` is always 1 less than the exponent returned by std::frexp because of the different normalization requirements: for the exponent e returned by `std::logb`, |num*r-e
| is between 1 and r (typically between 1 and 2), but for the exponent e returned by std::frexp, |num*2-e
| is between 0.5 and 1.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::logb(num) has the same effect as std::logb(static_cast<double>(num)).

### Example

Compares different floating-point decomposition functions:

Run this code

    #include <cfenv>
    #include <cmath>
    #include <iostream>
    #include <limits>
    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        double f = 123.45;
        std::cout << "Given the number " << f << " or " << std::hexfloat
                  << f << std::defaultfloat << " in hex,\n";

        double f3;
        double f2 = std::modf(f, &f3);
        std::cout << "modf() makes " << f3 << " + " << f2 << '\n';

        int i;
        f2 = std::frexp(f, &i);
        std::cout << "frexp() makes " << f2 << " * 2^" << i << '\n';

        i = std::ilogb(f);
        std::cout << "logb()/ilogb() make " << f / std::scalbn(1.0, i) << " * "
                  << std::numeric_limits<double>::radix
                  << "^" << std::ilogb(f) << '\n';

        // error handling
        std::feclearexcept(FE_ALL_EXCEPT);

        std::cout << "logb(0) = " << std::logb(0) << '\n';
        if (std::fetestexcept(FE_DIVBYZERO))
            std::cout << "    FE_DIVBYZERO raised\n";
    }

Possible output:

    Given the number 123.45 or 0x1.edccccccccccdp+6 in hex,
    modf() makes 123 + 0.45
    frexp() makes 0.964453 * 2^7
    logb()/ilogb() make 1.92891 * 2^6
    logb(0) = -Inf
        FE_DIVBYZERO raised

### See also

frexpfrexpffrexpl (C++11)(C++11) | decomposes a number into significand and base-2 exponent (function)
ilogbilogbfilogbl (C++11)(C++11)(C++11) | extracts exponent of the number (function)
scalbnscalbnfscalbnlscalblnscalblnfscalblnl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11) | multiplies a number by FLT_RADIX raised to a power (function)
C documentation for logb

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